Britain, the United States and France are to table a UN Security Council resolution on Syria today, David Cameron told MPs on Tuesday afternoon.
Appearing before the Commons liaison committee, the prime minister said the Russian proposal that the regime of Bashar al-Assad could turn his chemical weapons over the "international control" was an "interesting proposal if it is serious".
Cameron said it would "achieve a major goal we have as a government to get rid of chemical weapons" as Syria has the largest stockpile in the world.
The prime minister told MPs he had spoken with president Obama and that the UN resolution was designed to make sure the Russian proposal was not simply a "ruse" designed to delay action by the West against Assad.
"We need to know there is a proper timetable for doing this. There will have to be consequences if it isn't done," he said. "Of course we should be sceptical, of course we should not forget a war crime has been committed, but this could be a major step forward."
However the AFP news agency has reported that Russia is opposed to UN resolution on Syria.
Cameron also insisted that the proposal would not have been made had the United States and others had not threatened military action. "None of this would be happening if there wasn't serious international pressure, led by the US, on Syria," he said.
"If we can achieve the removal and destruction of the biggest chemical weapons arsenal in the world that would be a significant step forward. We must enter this with a very hard head and some pretty cool calculations."
On Tuesday president Obama said he will put plans for a military strike against Syria on hold if the country places all of its chemical weapons for destruction under international control.
Russian foreign minister Sergei Lavrov's proposal was made just hours after US secretary of state John Kerry suggested in London that Assad might forestall international military action by giving up his chemical arsenal.
Even though Kerry made clear that he had no expectation of Assad taking this step, Russia seized on the idea as a potential solution to the current impasse over the international community's response to the use of nerve gas sarin against civilians in a suburb of Damascus on August 21, which killed 1,429 people. Lavrov surprise proposal was immediately backed by Damascus yesterday.